Chiral Symmetry Breaking. Schwinger-Dyson Equations

Transcription

1 Critical End Point of QCD Phase-Diagram: A Schwinger-Dyson Equation Perspective Adnan Bashir Michoacán University, Mexico Collaborators: E. Guadalupe Gutiérrez, A Ahmad, A. Ayala, A. Raya, J.R. Quintero II Workshop on Perspectives in Non Perturbative QCD May 12-13, 13, 2014

2 Introduction Contents QCD at Zero Temperature Chiral Symmetry Breaking Confinement Light Quark Flavors and Interaction Strength QCD at Finite Temperature and Chemical Potential Propagators and Vertices Chiral Symmetry Restoration Concluding Remarks

3 Introduction Hadron Physics QCD Phase Diagram (T, ) Magnetic Catalysis(,eB) Running Quark Mass (,N f ) Chiral Symmetry Breaking Condensed Matter Systems (x,v F,, ) Schwinger-Dyson Equations

4 QCD at Zero Temperature

5 QCD at Zero Temperature The QCD Lagrangian:

6 QCD at Zero Temperature 1000 MeV 5 MeV We can trace the origin of 98% of the luminous matter to QCD interactions. QCD

7 QCD at Zero Temperature Infrared Increase 0.2 fm 0.02 fm fm Asymptotic Freedom

8 QCD at Zero Temperature Parity Partners & Chiral Symmetry Breaking

9 The quark propagator: QCD at Zero Temperature Enhanced infrared Effective interaction

10 QCD at Zero Temperature Confinement: Can be inferred from the analytic properties of the propagator. Violation of the axiom of reflection positivity

11 QCD at Zero Temperature No. of light quark flavors also determine the extent of chiral symmetry breaking and confinement. AB, A. Raya, J. Rodrigues-Quintero, Phys. Rev. D (2013).

12 QCD at Zero Temperature Increasing no. of light quark flavors restores chiral symmetry and triggers deconfinement. Chiral condensate Confinement AB, A. Raya, J. Rodrigues-Quintero, Phys. Rev. D (2013).

13 QCD at Finite Temperature Fermi: Notes on Statistics and Thermodynamics ( ).

14 QCD at Finite Temperature

15 QCD at Finite Temperature

16 QCD at Finite Temperature Some lattice result at μ=0.

17 Facts and Challenges The theory at the edges is better understood. Lattice QCD and SDE find a rapid & smooth cross-over over at large T and μ B =0. Various models find a strong 1 st order phase transition at large μ B and T=0. 1 st order line originating at T=0 cannot end at μ B =0 as it is a cross- over. There must exist A critical end point.

18 Facts and Challenges A sound theoretical prediction for the existence and location of the critical end point on the QCD phase diagram is a challenging task. Are the two phase transitions, corresponding to confinement and deconfinement & chiral symmetry breaking and its restoration, coincidental? As they both owe themselves to the diminishing of the QCD interaction strength, one may expect them to chart out the same curve in the QCD phase diagram. AB, A. Raya, I.C. Cloet, C.D. Roberts, Phys. Rev. C (2008) [QED3, N f ] AB, A. Raya, J. Rodríguez, Phys. Rev. D (2013) [QCD, N f ]

19 Schwinger-Dyson Equations Charting out the phase diagram from the basic building blocks of QCD is an outstanding problem. Through SDEs, the fundamental equations of QCD, we can attack the problem through first principles in the continuum. Schwinger-Dyson Equations combine the non-perturbative regime of a theory with its perturbative limit naturally. Thus they provide an ideal frame-work to study the the transition region in QCD phase diagram where non perturbative phenomena of chiral symmetry breaking and confinement melt away. -X Qin, L. Chang, H. Chen, Y-X Liu, C.D. Roberts, Phys. Rev. Lett (2011).S. Fischer, J. Luecker, Phys. Lett. B (2013)

20 Schwinger-Dyson Equations Quark Propagator: At finite T and μ, its general form is: Its solution for the scalar functions A,B and C can be obtained by solving the SDE:

21 Gluon Propagator: Schwinger-Dyson Equations We follow the lead of Qin et. al.: S. Qin. L. Chang, C.D. Roberts, Y.X. Liu, Phys. Rev. Lett (2011)

22 Schwinger-Dyson Equations Quark-Gluon Vertex:

23 Quark-Gluon Vertex: Schwinger-Dyson Equations Perturbative HTL constraints have been calculated in: A. Ayala, AB, Phys. Rev. D (2001) We make a modest but practical ansatz: and fix D(T) to match lattice results along the μ=0 axis.

24 Chiral Symmetry Restoration A. Bazavov et. al., Phys. Rev. D (2012)

25 Chiral Symmetry Restoration Chiral symmetry restoration also manifests itself in the function D(T). The critical temperature obtained from the behavior of D(T) is GeV whereas the obtained from the condensate is GeV.

26 Chiral Symmetry Restoration Knowing D(T), we can repeat the exercise of computing the condensate off the μ=0 axis. E. Gutiérrez, A. Ahmad, A. Ayala, AB, A. Raya, J. Phys. G (2014)

27 Chiral Symmetry Restoration We plot our order parameter - T <ψψ ψψ>, and look at the plot for each μ. The maximum gives the pseudo critical point (T c,μ c ).

28 Chiral Symmetry Restoration The critical line and the critical end point.

29 Chiral Symmetry Restoration At chemical potential μ~0.22 GeV, the thermodynamic singularity arisen from disjointed condensate can be identified with the onslaught of 1 st order phase transition.

30 Concluding Remarks Exploiting the lattice results for the temperature evolution of the quark-anti anti-quark condensate, we use the Schwinger-Dyson equations to compute the same along the μ axis. The temperature derivative of the quark-anti anti-quark condensate has a smooth and finite maximum for μ~0. As μ increases, this maximum starts growing and shoots up to infinity for μ~0.22 GeV. We identify this thermodynamic singularity with a change of the nature of phase transition from a simple cross-over over to a 1st order phase transition. Studying the analytic properties of the quark propagator, the confinement-deconfinement phase transitions appears to chart out the similar curve in the QCD phase diagram.